Question

You have won a small lottery in which you will receive a series of payments forever. The payments start at $800 received today and grow effectively at 3.25% a year forever. Given an APR of 5.25% compounded quarterly, what is the present value of your lottery winnings?

Question 10 options:

$40,054

$41,055

$42,057

$43,058

$44,059

Answer 1

Answer is $40,054

First Payment = $800
Growth Rate = 3.25%

Annual Interest Rate = 5.25% compounded quarterly

Quarterly Interest Rate = 5.25% / 4
Quarterly Interest Rate = 1.3125%

Effective Annual Rate = (1 + Quarterly Interest Rate)^4- 1
Effective Annual Rate = (1 + 0.013125)^4 - 1
Effective Annual Rate = 1.0535427 - 1
Effective Annual Rate = 0.0535427 or 5.35427%

Present Value of Winnings = First Payment * (1 + Effective Annual Rate) / (Effective Annual Rate - Growth Rate)
Present Value of Winnings = $800 * 1.0535427 / (0.0535427 - 0.0325)
Present Value of Winnings = $800 * 1.0535427 / 0.0210427
Present Value of Winnings = $40,054

Therefore, the present value of your lottery winnings is $40,054